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arXiv · 2307.07825

Why is my rational Painlev\'e V solution not unique?

H. Aratyn·J. F. Gomes·G. V. Lobo·A. H. Zimerman
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Abstract

Under special conditions the Painlev\'e V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbits of the fundamental shift operators of $A^{(1)}_{3}$ affine Weyl group with rational solutions we derive conditions for such non-uniqueness to occur. We identify the seed solutions from which the non-unique solutions are generated and put forward a method to systematically obtain their closed expressions from the underlying seed solutions.

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H. Aratyn, J. F. Gomes, G. V. Lobo, A. H. Zimerman. 2023-07-15. Why is my rational Painlev\'e V solution not unique?. https://arxiv.org/abs/2307.07825

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